| Title | An Introduction to Optimal Data Collection for Geophysical Model Calibration Problems |
|---|---|
| Authors | R. Nicholson, H. Alferink, E. Paton-Simpson, M. Gravatt, S. Guzman, J. Popineau, J.P. O’Sullivan, M.J. O’Sullivan, O.J. Maclaren |
| Year | 2020 |
| Conference | New Zealand Geothermal Workshop |
| Keywords | Calibration, estimation, inversion, Bayesian, data collection, optimization, uncertainty quantification, uncertainty reduction |
| Abstract | Computational modelling and calibration can play a vital role in various geophysical settings, including the management of geothermal reservoirs. The calibration process typically involves perturbing model parameters, such as subsurface permeabilities, so that the resulting simulator outputs match field data, usually consisting of noisy surface or subsurface measurements. In an engineering context, however, model calibration is not a once-off process, but rather an on-going process that often requires careful decision-making about whether to collect new measurements and where these should be collected. Here we present a tutorial-style introduction on how to formulate and solve such decision problems, using two archetypal but straightforward geophysical model problems. The basic calibration problem can be considered a statistical inference problem. In particular, the Bayesian framework for calibration naturally allows for uncertainties in the data, the parameters, and models to be quantified and incorporated into this process. In this framework, the solution to the calibration (and inference problem) is a so-called posterior probability density, which characterises the remaining uncertainty in the parameters after conditioning on the field data. This uncertainty can then help guide the management of geophysical resources, where, intuitively, reducing (posterior) uncertainty enables higher quality decisions to be made. Reduction in posterior uncertainty is achievable by a) improving measurement precision at existing locations and hence obtaining similar data with lower noise or b) collecting additional data at new locations. Here we focus on the second option. The cost of collecting data in new areas can be considerable, however, especially when this data requires e.g. drilling a new observation well or constructing and deploying other expensive measurement equipment. Hence, we consider the design problem of how to determine the reward, in terms of uncertainty reduction, of a potential new observation, before collection. In addition to illustrating the basic principles of optimal data collection and data worth analysis using simple geophysical problems, we also show how the methodology used can be further developed to include, for example, the possibility of spatially heterogeneous costs of acquiring new data. |